Details

Time bar (total: 46.0s)

sample211.0ms

Algorithm
intervals
Results
102.0ms73×body1280valid
35.0ms82×body640valid
26.0ms296×body80valid
12.0ms43×body320valid
5.0ms25×body160valid

simplify24.6s

Counts
1 → 1
Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
01415
12414
24514
39014
418914
528114
635814
749314
864614
9103114
10180014
11258614
12324314
13356414
14364814
done364814

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.7b

localize32.0ms

Local error

Found 3 expressions with local error:

0.0b
(* J (- (exp l) (exp (- l))))
0.0b
(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)))
6.6b
(- (exp l) (exp (- l)))

rewrite207.0ms

Algorithm
rewrite-expression-head
Rules
31×add-sqr-sqrt
29×*-un-lft-identity
27×prod-diff
25×add-cube-cbrt
11×distribute-rgt-in distribute-lft-in
10×pow1 add-exp-log add-cbrt-cube
8×associate-*r*
5×add-log-exp
4×associate-*r/ associate-*l* pow-prod-down prod-exp cbrt-unprod
3×expm1-log1p-u sub-neg flip3-- fma-neg flip-- log1p-expm1-u
2×associate-*l/ *-commutative distribute-lft-out-- difference-of-squares
1×diff-log unswap-sqr
Counts
3 → 96
Calls
3 calls:
76.0ms
(* J (- (exp l) (exp (- l))))
99.0ms
(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)))
28.0ms
(- (exp l) (exp (- l)))

series307.0ms

Counts
3 → 9
Calls
3 calls:
82.0ms
(* J (- (exp l) (exp (- l))))
170.0ms
(* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)))
55.0ms
(- (exp l) (exp (- l)))

simplify3.4s

Counts
105 → 105
Iterations

Useful iterations: 3 (1.6s)

IterNodesCost
01682051
13431619
29351258
341661093
done50001093

prune356.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize30.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0))) U)
0.0b
(fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))
0.1b
(* (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)))

rewrite88.0ms

Algorithm
rewrite-expression-head
Rules
8×pow1 add-exp-log add-cbrt-cube
5×add-log-exp
4×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
3×expm1-log1p-u associate-*r* pow-prod-down prod-exp cbrt-unprod log1p-expm1-u
1×+-commutative fma-def flip3-+ associate-*l* sum-log *-commutative flip-+ fma-udef
Counts
3 → 44
Calls
3 calls:
37.0ms
(+ (* (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0))) U)
1.0ms
(fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))
48.0ms
(* (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)))

series679.0ms

Counts
3 → 9
Calls
3 calls:
375.0ms
(+ (* (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0))) U)
89.0ms
(fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))
215.0ms
(* (* J (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))) (cos (/ K 2.0)))

simplify1.1s

Counts
53 → 53
Iterations

Useful iterations: done (1.1s)

IterNodesCost
0981335
12391262
28911113
done50011066

prune403.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* J (* (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))) (cos (/ K 2.0)))) U)
0.0b
(fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))
0.1b
(* J (* (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))) (cos (/ K 2.0))))
0.1b
(* (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))) (cos (/ K 2.0)))

rewrite91.0ms

Algorithm
rewrite-expression-head
Rules
11×pow1 add-exp-log add-cbrt-cube
9×add-sqr-sqrt
7×add-cube-cbrt *-un-lft-identity
6×associate-*l* add-log-exp
4×expm1-log1p-u associate-*r* pow-prod-down prod-exp cbrt-unprod log1p-expm1-u
2×*-commutative
1×+-commutative fma-def flip3-+ sum-log flip-+ fma-udef unswap-sqr
Counts
4 → 64
Calls
4 calls:
37.0ms
(+ (* J (* (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))) (cos (/ K 2.0)))) U)
1.0ms
(fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))
42.0ms
(* J (* (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))) (cos (/ K 2.0))))
9.0ms
(* (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))) (cos (/ K 2.0)))

series904.0ms

Counts
4 → 12
Calls
4 calls:
395.0ms
(+ (* J (* (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))) (cos (/ K 2.0)))) U)
80.0ms
(fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l)))
285.0ms
(* J (* (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))) (cos (/ K 2.0))))
144.0ms
(* (fma 1/3 (pow l 3) (fma 1/60 (pow l 5) (* 2 l))) (cos (/ K 2.0)))

simplify1.1s

Counts
76 → 76
Iterations

Useful iterations: done (1.1s)

IterNodesCost
01201865
12881788
210441565
done50011508

prune507.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize55.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0))))
0.3b
(cbrt (cos (/ K 2.0)))
0.3b
(cbrt (cos (/ K 2.0)))
0.3b
(cbrt (cos (/ K 2.0)))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
15×add-cube-cbrt *-un-lft-identity
11×pow1
9×pow1/3
6×add-exp-log swap-sqr associate-*r* associate-*l*
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp unswap-sqr
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 81
Calls
4 calls:
24.0ms
(* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0))))
2.0ms
(cbrt (cos (/ K 2.0)))
2.0ms
(cbrt (cos (/ K 2.0)))
2.0ms
(cbrt (cos (/ K 2.0)))

series1.2s

Counts
4 → 12
Calls
4 calls:
482.0ms
(* (cbrt (cos (/ K 2.0))) (cbrt (cos (/ K 2.0))))
259.0ms
(cbrt (cos (/ K 2.0)))
206.0ms
(cbrt (cos (/ K 2.0)))
232.0ms
(cbrt (cos (/ K 2.0)))

simplify2.1s

Counts
93 → 93
Iterations

Useful iterations: done (2.1s)

IterNodesCost
0741042
1138953
2306881
3675792
41743785
done5000743

prune616.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

regimes436.0ms

Accuracy

0% (0.2b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02022
12422
done2422

end0.0ms

sample7.4s

Algorithm
intervals
Results
2.3s2659×body1280valid
1.8s2604×body640valid
1.6s8459×body80valid
514.0ms1437×body320valid
511.0ms708×body160valid